Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

   1         3     3      2      1
           /     /      /       
     3     2     1      1   3      2
    /     /                        
   2     1         2                 3

方法一：递归（超时）

class Solution {
public:
    int numTrees(int n) {
        int sum = 0;
        if(n<=1) return 1;
        for(int i=0;i<n;i++){
            sum +=numTrees(i)*numTrees(n-1-i);
        }
       return sum;
    }
};

方法二：动态规划（AC）

class Solution {
public:
    int numTrees(int n) {
        int num[n+1];
        fill(num,num+n+1,0);
        num[0] = 1;
        num[1] = 1;
        num[2] = 2;
        for(int i=3; i<=n; i++){
            for(int j=1; j<=i; j++)
                num[i]+=num[j-1]*num[i-j];
           
        }
        return num[n];
    }
};